Waves of intermediate length through an array of vertical cylinders
We report a semi-analytical theory of wave propagation through a vegetated water. Our aim is to construct a mathematical model for waves propagating through a lattice-like array of vertical cylinders, where the macro-scale variation of waves is derived from the dynamics in the micro-scale cells. Ass...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Netherlands
2016
|
| Online Access: | http://hdl.handle.net/1721.1/104628 https://orcid.org/0000-0003-1487-9477 |
| _version_ | 1826212946994266112 |
|---|---|
| author | Chan, I. -Chi Liu, Philip L. -F. Mei, Chiang Chung |
| author2 | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Chan, I. -Chi Liu, Philip L. -F. Mei, Chiang Chung |
| author_sort | Chan, I. -Chi |
| collection | MIT |
| description | We report a semi-analytical theory of wave propagation through a vegetated water. Our aim is to construct a mathematical model for waves propagating through a lattice-like array of vertical cylinders, where the macro-scale variation of waves is derived from the dynamics in the micro-scale cells. Assuming infinitesimal waves, periodic lattice configuration, and strong contrast between the lattice spacing and the typical wavelength, the perturbation theory of homogenization (multiple scales) is used to derive the effective equations governing the macro-scale wave dynamics. The constitutive coefficients are computed from the solution of micro-scale boundary-value problem for a finite number of unit cells. Eddy viscosity in a unit cell is determined by balancing the time-averaged rate of dissipation and the rate of work done by wave force on the forest at a finite number of macro stations. While the spirit is similar to RANS scheme, less computational effort is needed. Using one fitting parameter, the theory is used to simulate three existing experiments with encouraging results. Limitations of the present theory are also pointed out. |
| first_indexed | 2024-09-23T15:40:59Z |
| format | Article |
| id | mit-1721.1/104628 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:40:59Z |
| publishDate | 2016 |
| publisher | Springer Netherlands |
| record_format | dspace |
| spelling | mit-1721.1/1046282022-09-29T15:28:37Z Waves of intermediate length through an array of vertical cylinders Chan, I. -Chi Liu, Philip L. -F. Mei, Chiang Chung Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Mei, Chiang Chung We report a semi-analytical theory of wave propagation through a vegetated water. Our aim is to construct a mathematical model for waves propagating through a lattice-like array of vertical cylinders, where the macro-scale variation of waves is derived from the dynamics in the micro-scale cells. Assuming infinitesimal waves, periodic lattice configuration, and strong contrast between the lattice spacing and the typical wavelength, the perturbation theory of homogenization (multiple scales) is used to derive the effective equations governing the macro-scale wave dynamics. The constitutive coefficients are computed from the solution of micro-scale boundary-value problem for a finite number of unit cells. Eddy viscosity in a unit cell is determined by balancing the time-averaged rate of dissipation and the rate of work done by wave force on the forest at a finite number of macro stations. While the spirit is similar to RANS scheme, less computational effort is needed. Using one fitting parameter, the theory is used to simulate three existing experiments with encouraging results. Limitations of the present theory are also pointed out. Cornell University (Mary Upson visiting professorship) 2016-09-30T21:30:05Z 2016-09-30T21:30:05Z 2013-09 2013-05 2016-08-18T15:20:35Z Article http://purl.org/eprint/type/JournalArticle 1567-7419 1573-1510 http://hdl.handle.net/1721.1/104628 Mei, Chiang C., I. -Chi Chan, and Philip L. -F. Liu. “Waves of Intermediate Length through an Array of Vertical Cylinders.” Environmental Fluid Mechanics 14.1 (2014): 235–261. https://orcid.org/0000-0003-1487-9477 en http://dx.doi.org/10.1007/s10652-013-9308-1 Environmental Fluid Mechanics Creative Commons Attribution-NonCommercial-Share Alike http://creativecommons.org/license/by-nc-sa/4.0/ Springer Science+Business Media Dordrecht application/pdf Springer Netherlands Springer Netherlands |
| spellingShingle | Chan, I. -Chi Liu, Philip L. -F. Mei, Chiang Chung Waves of intermediate length through an array of vertical cylinders |
| title | Waves of intermediate length through an array of vertical cylinders |
| title_full | Waves of intermediate length through an array of vertical cylinders |
| title_fullStr | Waves of intermediate length through an array of vertical cylinders |
| title_full_unstemmed | Waves of intermediate length through an array of vertical cylinders |
| title_short | Waves of intermediate length through an array of vertical cylinders |
| title_sort | waves of intermediate length through an array of vertical cylinders |
| url | http://hdl.handle.net/1721.1/104628 https://orcid.org/0000-0003-1487-9477 |
| work_keys_str_mv | AT chanichi wavesofintermediatelengththroughanarrayofverticalcylinders AT liuphiliplf wavesofintermediatelengththroughanarrayofverticalcylinders AT meichiangchung wavesofintermediatelengththroughanarrayofverticalcylinders |